Time-dependent development of interface morphology from initial perturbation of a planar interface to a steady periodic array of cells or dendrites was directly observed during directional solidification brocess of a transparent model alloy, succinonitrile -1.1 wt% ethanol. The following results are obtained: 1) The measured wavelength of initial perturbation of planar interface instability is within the expected wavelength range by the MS theory, but not the same as the expected wavelength with the fastest amplitude developing speed. 2) During the initial stage of a planar interface instability, the developing speed of perturbation amplitude is indeed a linear function of the amplitude, but the measured value of the amplitude developing rate is much smaller than the theoretical value. 3) The features of morphology development of cells and dendrites are different from each other, and the main cause leading to the different developing behaviour is that the relative scale of the steady primary spacing and the initial perturbation wavelength is different in the two cases.